Unless otherwise indicated herein, the approaches described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section.
An accurate bandgap voltage is required as a reference voltage in many applications. For example, a Digital to Analog Converters (DAC) and an Analog to Digital Converters (ADC) requires an accurate voltage reference. Output power measurement and calibration in a transmitter circuit is another example where an accurate voltage reference is required.
FIG. 1 shows an example of an automatic power control circuit 100 that employs a bandgap voltage reference. A digital block 102 generates an output which feeds into a transmitter 104. A power amplifier 106 amplifies the power of the signal produced by the transmitter 104. A coupler 108 couples the output of the power amplifier 106 to a switch 110 for transmission via an antenna 112. The coupler 108 provides a second output that goes into a detector 114, which detects a power level of the transmitter 104. An output of the detector 114 may be a DC voltage level VDET that is proportional to the detected power level. The VDET is compared to a reference voltage VREF that can be provided by a bandgap voltage reference circuit 116; e.g., using a comparison block 118. A voltage level output of the comparison block 118 is converted to a digital signal by an ADC 120. The digital signal may then serve as a power level feedback signal that the digital block 102 may use to subsequently adjust a transmission power level or some other aspect of the operation of the digital block. It can be appreciated that proper operation of the power control circuit 100 requires an accurate voltage reference VREF. A bandgap voltage reference is thus an important circuit in many mixed-signal analog-digital and radio-frequency systems. It is not possible to make a precise comparison or conversion if the bandgap voltage reference is not constant.
Referring to FIG. 2, a typical bandgap voltage reference circuit is shown. The circuit typically includes two p-n junctions having different current densities. The circuit in FIG. 2, for example, the p-n junctions are provided by diodes D1 and D2 of different sizes, where the size of D2 is greater than the size of D1. An op-amp controls (via output Vg) two current sources to generate a current IC that is Proportional To the Absolute Temperature (PTAT) in a first resistor (e.g., R1) and to bias two diodes (D1 and D2). This forces a voltage VBE1 to be the same as a sum of voltages VBE2+VR1. The op-amp output (Vg) also controls a third current source to generate the current IC to produce a voltage in a second resistor (e.g., R2) and bias another diode (D3). This voltage drop across R2 is added to the voltage across another p-n junction (e.g., diode D3) to generate the band-gap voltage (VBG).
When a diode that is operated at constant current (e.g., where current does not depend on any process corner from one chip to another), the voltage across that diode is inversely proportional (Complementary) To Absolute Temperature (CTAT); i.e., the voltage decreases with increasing temperature. Here, the constant current is the PTAT current IC, which is only dependent on the temperature. If the ratio between the first resistor (R1) and the second resistor (R2) is chosen properly, the first order effects of the temperature dependency of the diode D3 and the PTAT current IC will cancel out. In other words, the negative slope (negative temperature coefficient) of the voltage vs. temperature curve of diode D3 (VBE3) is compensated by the positive slope (positive temperature coefficient) of the temperature variation of a voltage difference between the diodes D1 and D2, namely (AVBE1,2=VBE1−VBE2).
The output voltage VBG of the circuit shown in FIG. 2 is obtained as follows:VBG=VBE3+IC×R2,  Eqn. 1where VBG is the bandgap voltage,
VBE3 is the voltage across diode D3,
Ic is the current generated by the current source, and
R2 is the resistance of the resistor R2.
The op-amp will force VBE1 to be same as VBE2+IC×R1 and so:IC×R1=VBE1−VBE2=ΔVBE1,2,  Eqn. 2where VBE1 and VBE2 are voltages across respective diodes D1 and D2. A diode is typically fabricated using a bipolar transistor by connecting together the base and collector of the transistor. For a bipolar transistor (and therefore for the diode), the collector current (IC) can be expressed as:IC=Is×e(VBE/VT),  Eqn. 3where IS is the saturation current for the bipolar transistor, and
VT is equal to
      kT    q    ,where k is the Boltzmann constant, q is the electron charge, and T is absolute temperature in units of Kelvin.
Therefore, the difference between the base-emitter voltages (ΔVBE1,2) of two bipolar transistors configured as diodes D1 and D2 can be expressed as:
                                                        I              C                        ⨯                          R              1                                =                                                    V                                  BE                  ⁢                                                                          ⁢                  1                                            -                              V                                  BE                  ⁢                                                                          ⁢                  2                                                      =                                          Δ                ⁢                                                                  ⁢                                  V                                                            BE                      ⁢                                                                                          ⁢                      1                                        ,                    2                                                              =                                                V                  T                                ⁢                                  ln                  ⁡                                      (                                                                                            I                                                      C                            ⁢                                                                                                                  ⁢                            1                                                                          /                                                  I                                                      S                            ⁢                                                                                                                  ⁢                            1                                                                                                                                                I                                                      C                            ⁢                                                                                                                  ⁢                            2                                                                          /                                                  I                                                      S                            ⁢                                                                                                                  ⁢                            2                                                                                                                )                                                                                      ,                                  ⁢                              I                          C              ⁢                                                          ⁢              1                                =                                    I                              C                ⁢                                                                  ⁢                2                                      =                          I              C                                      ,                            Eqn        .                                  ⁢        4            where IS1 and IS2 are the saturation currents respectively for the bipolar transistors used to form diodes D1 and D2 (e.g., see inset in FIG. 6), and IC1 and IC2 are currents through respective diode D1 and diode D2. Recalling that diode D2 is larger than diode D1, we have IS2=IS1×N, where N is the ratio of the size of diode D2 to the size of diode D1. Eqn. 4 can be expressed as:IC×R1=ΔVBE1,2=VTln(N).  Eqn. 5Therefore, we can re-write Eqn. 1, as follows:
                              V          BG                =                                            V                              BE                ⁢                                                                  ⁢                3                                      +                                          (                                                      R                    2                                    /                                      R                    1                                                  )                            ×              Δ              ⁢                                                          ⁢                              V                                                      BE                    ⁢                                                                                  ⁢                    1                                    ,                  2                                                              =                                    V                              BE                ⁢                                                                  ⁢                3                                      +                                                            R                  2                                                  R                  1                                            ×                              V                T                            ⁢                              ln                ⁡                                  (                  N                  )                                                                                        Eqn        .                                  ⁢        6            A suitable bandgap voltage reference is as a voltage that does not change over temperature (T), which can be expressed in the following way: δVBG/δT=0. To calculate δVBG/ΔT, first we need to know how saturation current IS changes versus temperature. In other words:
                              I          S                =                  b          ×                      T                          4              +              m                                ⁢                      exp            ⁡                          (                                                -                                      E                    g                                                  kT                            )                                                          Eqn        .                                  ⁢        7            where IS is saturation current,
b is proportional to size of the bipolar transistor,
m is about −1.5, and
Eg is the band-gap energy of silicon material, with which the bipolar transistor is made up and is equal to 1.12 eV (eV is electron voltage).
Next, we calculate the variation of δ(ΔVBE1,2)/δT with the help of Eqn. 5:
                                          ∂                          (                              Δ                ⁢                                                                  ⁢                                  V                  BE                                            )                                            ∂            T                          -                              k            q                    ⁢                                    ln              ⁡                              (                N                )                                      .                                              Eqn        .                                  ⁢        8            Now, we calculate the variation of VBE of δVBE/δT using Eqns. 3 and 7:
                                          ∂                          V              BE                                            ∂            T                          =                                                            V                BE                            -                                                (                                      3                    +                    m                                    )                                ⁢                                  V                  T                                            -                                                E                  g                                /                q                                      T                    .                                    Eqn        .                                  ⁢        9            With the help of Eqn. 6, the bandgap voltage variation versus temperature will be equal to:
                                          ∂                          V              BG                                            ∂            T                          =                                                            V                                  BE                  ⁢                                                                          ⁢                  3                                            -                                                (                                      3                    +                    m                                    )                                ⁢                                  V                  T                                            -                                                E                  g                                /                q                                      T                    +                                    (                                                R                  2                                /                                  R                  1                                            )                        ×                          k              q                        ⁢                                          ln                ⁡                                  (                  N                  )                                            .                                                          Eqn        .                                  ⁢        10            To have a fixed-band gap voltage that does not change with temperature, namely δVBG/δT=0, we have:
                              (                                    R              2                        /                          R              1                                )                =                              -                          (                                                                    V                                          BE                      ⁢                                                                                          ⁢                      3                                                        -                                                            (                                              3                        +                        m                                            )                                        ⁢                                          V                      T                                                        -                                                            E                      g                                        /                    q                                                  T                            )                                /                      (                                          k                q                            ⁢                                                ln                  ⁡                                      (                    N                    )                                                  .                                      )                                              Eqn        .                                  ⁢        11            Recalling that N is the ratio of the size of diode D2 to diode D1, the foregoing shows that the ratio of R2 to R1 needs to be selected depending on N in order to provide a bandgap voltage VBG that exhibits a small variation over temperature. However, as shown by Eqn. 11, the resistor ratio of R2/R1 also depends on the VBE3 (voltage drop of diode D3). This means that due to process variations (process corners) of internal devices (e.g., the transistors which comprise the diodes) of a bandgap voltage reference circuit (e.g., the transistors which comprise the diodes), the accuracy of the bandgap voltage reference circuit will not be consistent from one chip to another, and therefore accurate measurement in many applications that use band-gap voltage can become degraded from one chip to another chip.
FIG. 2A illustrates an example of another conventional band-gap circuit where the current branch comprising the current source, resistor R2, and diode D3 may be replaced. Instead, a resistor R4 equal to R2−R1 is added in series with resistor R1. Both R2 and R4 may consist of a resistor array (see, for example, FIG. 2B), and may be adjusted by a calibration circuit (not shown). The value of R4 is the difference between the R2-array, and R1. Here the bandgap voltage VBG may be defined by Eqn. 6, but instead of VBE3 we will have VBE2.
The term “process corner” refers to variations in fabrication parameters on a semiconductor wafer of an integrated circuit. Process corners represent the extremes of these parameter variations within which the circuit must function correctly. A chip (e.g., a circuit design that includes a bandgap reference voltage generator) is typically fabricated on a wafer along with multiple other copies of the chip. The process corners of devices (e.g., transistors) on a given chip are essentially the same to within a small degree of variation. However, due to process variations across the wafer, the process corners of devices between chips on the same wafer may vary significantly. For example, the devices on one chip may be “fast”, while the same devices on another chip may be “slow”.
In the case of a bandgap voltage reference circuit, if the ratio of R2 to R1 is set for so-called “nominal” process corners, then chips whose devices have nominal process corners will behave as intended; in other words, their output voltage will vary within an acceptable range with changes in the ambient temperature. However, bandgap voltage reference circuits in chips that have fast or slow process corners, or any process corner other than a nominal process corner, may exhibit a wide swing in output voltage with changes in ambient temperature. Referring to FIG. 3, for example, a simulation is shown for bandgap voltage versus temperature for three typical process corners: fast, nominal, and slow. As can be seen, the voltage variation for a chip having nominal process corners, over a 120° C. temperature variation, is very small (e.g., <4 mV). The voltage variation for a slow corner chip over the same temperature range is high (e.g., >−9.3 mV, from low temperature to high temperature), and for a fast corner chip is also high (e.g., +7 mV). The bandgap voltage variation at nominal 27° C. temperature (equal to T=300° K) for different chip (for e.g. a fast-corner chip to a slow-corner chip) is very high as well.
Typically, manufacturers will use a programmable resistor array 202 (e.g., FIG. 2B) for one of the resistors, for example, resistor R2. The manufacturer can measure one or more parameters in each part and program the resistor array 202 in order to attain a suitable ratio of R2 to R1 according to the measurements. For example, a conventional approach is to measure a specific parameter (usually some reference voltage) for each part during a calibration process and burn some fuses of the resistor array 202 to set the switches of the resistor array to the OPEN or CLOSE thereby adjusting the value of R2 to attain the required R2/R1. This process tends to increase the calibration time for each part, and leads to increased cost.